In this paper, we investigate the spectral response of whispering-gallery-mode (WGM) resonators coupled to their access waveguide with a view to design their constitutive waveguides to promote critical-coupling over a wide spectral range and thereby facilitate their use for high-sensitivity sensing or nonlinear frequency conversion applications. The carried-out theoretical analysis is based on the universal response functions of singlemode and unidirectional devices. A coupled-mode treatment of the coupling region enables to derive two sets of favorable designs. The identified resonator/access waveguide systems exploit waveguides with mismatched propagation constants forming a coupling section exhibiting either an achromatic beat-length or an achromatic power-transfer coefficient. This generic model is followed by a numerical case study of vertically-coupled Si3N4 racetrack resonators. The conventional (quasi-)phase-matched configuration, treated as a reference case, is shown to display a critical-coupling bandwidth of 23 nm at a wavelength of 1550nm, whereas the proposed new designs demonstrate critical bandwidths larger than 330nm, i.e. exhibit bandwidths enhanced by more than one order of magnitude.
In this article, we apply the coupled-mode theory to vertically-coupled micro-disk resonators presenting an asymmetric distribution of refractive index and a multilayer separation region between the two waveguide cores, resulting in an effective propagation constant phase-mismatch in the coupling region. We introduce a criterion which, given the coupler overall permittivity distribution, clarifies how to best choose the individual decomposition index profiles among the various possible solutions. Following our recent experimental demonstration we subsequently exploit the derived decomposition to evaluate the theoretical transmission characteristics of an AlGaAs/AlOx-based structure as function of wavelength and as function of the position of the resonator relative to the access waveguide.We show that the resonant dips of the intensity transmission, spaced by the cavity FSR, are modulated by an envelop which governs the coupling regime of the resonator-waveguide system.
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This article reports the experimental and theoretical assessments of the optical characteristics of recently-introduced vertically-coupled microdisk resonators made by selective oxidation of AlGaAs multilayer structures. Experimental measurements show that the Q-factors are in the 10 3 to 10 4 range for diameters ranging from 75 to 300 µm. To establish the origins of this limited performance a coupled-mode-theory-based model of the single-access-waveguide-coupled resonator system was developed. It includes features which are specific to oxide-based vertically-coupled resonators, namely losses towards the slab waveguide lying under the resonator and a coupling region with an asymmetric and multilayer structure. Setting this simulation tool required the proposal and validation of a general criterion to select an appropriate set of decomposition permittivity profiles to be able to accurately model the characteristics of these more complex couplers using the coupled-mode-theory approach. This theoretical development is generic and can be now deployed to simulate any device which includes multi-waveguide couplers with arbitrary piece-wise-constant profile of the dielectric permittivity. Exploiting this particular development and experimental measurements of the disk sidewall roughness and of the coupling lengths, the calculated and experimental Q-factors are found to be in good agreement and allow establishing that the current performance is limited by the scattering losses and the slab-leakage losses for small-and large-diameter devices respectively.
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